Analyze

Problem 1

Find when balls A and B, rotating at different speeds, meet at the starting point again. A: 2 rotations in 26 min, B: 5 in 35 min.

See Solution

Problem 2

Two discs with masses $m$ and $4m$ and radii $a$ and $2a$ roll without slipping. True statements? (A) Angular speed of center of mass is $\omega / 5$ (B) Angular momentum about $O$ is $81 m a^{2} \omega$ (C) Angular momentum about center of mass is $17 ma^{2} \omega / 2$ (D) $z$ -component of $\vec{L}$ is $55 m a^{2} \omega$

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Problem 3

Find when balls A and B, with rotation times of 26/2 and 35/5 minutes, meet at the starting point again.

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Problem 4

In the 2017 Wyoming senate of 30 members, find the inequality for Democrats $d$ and Republicans $r$ for a bill to pass:
A) $d+r>15$
B) $d+r<15$
C) $d+r \geq 15$
D) $d+r \leq 15$

See Solution

Problem 5

In the 2017 Wyoming state senate of 30 members, what inequality shows $d + r > 15$ for a bill to pass? A) $d+r>15$ B) $d+r<15$ C) $d+r \geq 15$ D) $d+r \leq 15$

See Solution

Problem 6

Find the focus of the parabola $x = y^{2} + 4y + 10$ . Choose from: $(-6.25,2)$ , $(-2,6.25)$ , $(6.25,-2)$ , $(2,6.25)$ .

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Problem 7

Find $k$ such that $x^{2}+k(x+2)+3(x+1)>0$ for all $x$ . What is the range of $k$ ?

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Problem 8

Find the largest prime $k$ such that $x^{2} + 6x + 25 - 2kx > 0$ for all real $x$ .

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Problem 9

Find the derivative of $x^{2}$ with respect to $x$ .

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Problem 10

In triangle $D E F$ , find the longest side given $m \angle D=59^{\circ}, m \angle E=76^{\circ}, m \angle F=45^{\circ}$ .

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Problem 11

Find the ball's instantaneous velocity at $t=10.0$ s given $x(t)=0.000015 t^{5}-0.004 t^{3}+0.4 t$ .

See Solution

Problem 12

Determine if the series converges or diverges: $\sum_{n=1}^{\infty}\left[\left(\frac{6}{7}\right)^{n}-\frac{3}{2^{n}}\right]$ . If it converges, find the sum.

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Problem 13

Determine if the series are convergent or divergent:
(I) $\sum_{n=1}^{\infty}\left(\frac{n+3}{2 n-5}\right)^{n}$
(II) $\sum_{n=1}^{\infty} \sqrt[4]{\frac{2}{n^{3}}}$
(III) $\sum_{n=1}^{\infty} \frac{2^{n}}{n ! \sqrt{n+1}}$
Explain your reasoning.

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Problem 14

Determine if these series converge or diverge, explaining your reasoning: (I) $\sum_{n=1}^{\infty}\left(\frac{n+3}{2 n-5}\right)^{n}$ , (II) $\sum_{n=1}^{\infty} \sqrt[4]{\frac{2}{n^{3}}}$ , (III) $\sum_{n=1}^{\infty} \frac{2^{n}}{n ! \sqrt{n+1}}$ .

See Solution

Problem 15

Determine if these series are absolutely convergent, conditionally convergent, or divergent:
(I) $\sum_{n=1}^{\infty}\left(\frac{\pi}{2}\right)^{n}$
(II) $\sum_{n=1}^{\infty} \frac{(-1)^{n-1} e}{\sqrt{n}}$
(III) $\sum_{n=1}^{\infty} \frac{1}{\sqrt{n}(\sqrt{n}+1)^{3}}$

See Solution

Problem 16

Find the values of $k$ such that the curve $y=x^{2}-4x+kx+3$ is above the line $y+3x=2$ .

See Solution

Problem 17

What time is nearest to midnight: A. 11:55 a.m., B. 12:06 a.m., C. 11:50 a.m., D. 12:03 a.m.?

See Solution

Problem 18

Find the range of values of $k$ for which the curve $y=x^{2}-4 x+k x+3$ is above the line $y+3 x=2$ .

See Solution

Problem 19

Find $a$ and $b$ if the line $y=x+h$ is tangent to $y=\frac{k}{1-x}$ and $k=\frac{(h+a)^{2}}{b}$ .

See Solution

Problem 20

Find values of $k$ so that $2 x^{2}+k^{2}+2-2(k+2) x > 0$ for all $x$ .

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Problem 21

Find the derivative $\frac{d}{d x}(\tan (\ln (x)))$ . What is $\frac{d y}{d x}$ for $\sqrt{x}+y^{2}=x y+2$ at (4,0)?

See Solution

Problem 22

A particle's velocity is $v(t)=e^{t-1}-3 \sin (t-1)$ . What is its motion at $t=1$ ? (a) speeding up, (b) slowing down, (c) neither, (d) at rest.

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Problem 23

At $t=2$ , what does $R^{\prime}(2)=4$ mean? (a) Depth is 4 inches. (b) Rate is 4 in/hr. (c) Rate of change is 4 in/hr². (d) Depth increased by 4 inches.

See Solution

Problem 24

Find the $x$ -coordinate of the inflection point of $f(x)=\int_{1}^{x}(3t-6t^{2})dt$ . Options: (a) $-\frac{1}{4}$ (b) $\frac{1}{4}$ (c) 0 (d) $\frac{1}{2}$ . Evaluate $\int \sin(3x)dx$ . Options: (a) $3\cos(3x)+C$ (b) $\frac{1}{3}\cos(3x)+C$ (c) $-3\cos(3x)+C$ (d) $-\frac{1}{3}\cos(3x)+C$ . Count removable discontinuities of $y=\frac{x+2}{x^{4}+16}$ . Options: (a) one (b) two (c) three (d) four.

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Problem 25

Which type of triangle cannot be both obtuse and one of the following: equilateral, acute, isosceles, or scalene?

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Problem 26

Which type of triangle cannot be both scalene and acute, right and acute, equilateral and acute, or isosceles and acute?

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Problem 27

已知 $z=1-2 i$ 且 $z+a \cdot \bar{z}+b=0$ ，求 $a$ 和 $b$ 的值。选项为 A. $a=1, b=-2$ B. $a=-1, b=2$ C. $a=1, b=2$ D. $a=-1, b=-2$ 。

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Problem 28

Identify the point that does not lie on the line formed by 3 of the following points: $(-2,-3)$ , $(3,2)$ , $(-1,0)$ , $(-3,-4)$ .

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Problem 29

已知半径为1的球体，求四棱锥体积最大时的高度选项：A. $\frac{1}{3}$ B. $\frac{1}{2}$ C. $\frac{\sqrt{3}}{3}$ D. $\frac{\sqrt{2}}{2}$

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Problem 30

Express $\tan 35^{\circ}+\tan 55^{\circ}$ using $k$ if $\cos 35^{\circ}=k$ .

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Problem 31

Calculate the total fuel cost from the transaction: 35.270 L at \$1.619/L, with HST included of \$6.57. Total: \$57.10.

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Problem 32

Identify the property shown: $E K + K F = K E + F K$ - multiplication, transitive, subtraction, reflexive, or none?

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Problem 33

Identify the property shown: $BK + KF = KE + FK$ (options: multiplication, transitive, subtraction, reflexive, none).

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Problem 34

Solve the equation: $x^{2}-16 x+61=2 x-20$ .

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Problem 35

In a survey of 400 Grade 7 students, find how many play both $\mathrm{ML}$ and $\mathrm{COD}$ using a Venn diagram.

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Problem 36

A car takes 4 s to stop over 20 m. Can we find its speed before braking without knowing acceleration? Options: (A) Yes, $20 \mathrm{~m} / 4 \mathrm{~s}$ . (B) Yes, double average speed. (C) No, need acceleration for $\Delta x=v_{0} t+\frac{1}{2} a t^{2}$ . (D) No, velocity definition includes acceleration.

See Solution

Problem 37

Identify the function: $y=-16x$ . Is it a step, constant, absolute value, or direct variation function?

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Problem 38

Identify the property shown in $3 x(y+2)=(y+2) 3 x$ : distributive, identity, commutative, or associative?

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Problem 39

Medina dan Adi bermain catur. Medina menang 3 kali dan draw 2 kali. Apakah pernyataan berikut benar atau salah?
1. Skor Adi = 21
2. Skor Medina = 44
3. Total skor = 52

See Solution

Problem 40

Medina menang 3 kali dan draw 2 kali. Cek kebenaran pernyataan: Skor Adi 21, Skor Medina 44, Total skor 52.

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Problem 41

Find series turns per pole for a compound generator to keep $V = 618 \mathrm{~V}$ with loads of $4 \mathrm{~A}$ and $5.5 \mathrm{~A}$ . Shunt turns: 2700.

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Problem 42

Tentukan apakah pernyataan berikut benar atau salah berdasarkan sifat asosiatif: $13 \times 7=7 \times 13$ , $9 \times(7-3)=(9 \times 7)-(9 \times 3)$ , $3 \times(5 \times 7)=(3 \times 5) \times 7$ , $[-50+160]: 4 \times(-2)$ .

See Solution

Problem 43

Which expression for $y$ comes from the system: $5x - 8y = 17$ and $-8x - 3y = -43$ ?

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Problem 44

Check if moments and forces are in equilibrium for a lever with a 30N pivot, 4N at 1m, and 7N at 3m.

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Problem 45

Ibrahim dan Zahra datang ke mesjid setiap 4 dan 6 hari. Apakah mereka bersama lagi pada 12, 14, dan 26 Juli 2022?

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Problem 46

Ibrahim dan Zahra datang bersama pada 2 Juli 2022. Kapan mereka akan bersama lagi? Tandai dengan $\sqrt{ }$ pilihanmu!
1. 12 Juli 2022
2. 14 Juli 2022
3. 26 Juli 2022
4. 7 Agustus 2022

See Solution

Problem 47

Analyze a lever with a pivot force of 30N. Left: 4N at 1m, 7N at 4m. Right: 7N at 3m. Determine:
a) Are moments in equilibrium? b) Are forces in equilibrium? c) Is the lever in equilibrium?

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Problem 48

Digite o número que falta na sequência: $1, 2, \square, 8, 16, 32$ .

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Problem 49

Analyze how a student could mistakenly choose each incorrect answer for the system of equations: $x - 2y = 2$ and $2x + y = 9$ .

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Problem 50

Solve the differential equation: $x y \, dx - (x+2) \, dy = 0$ .

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Problem 51

Find the equivalent expression for $9^{\frac{3}{4}}$ from the options: A) $\sqrt[3]{9}$ B) $\sqrt[4]{9}$ C) $\sqrt{3}$ D) $3 \sqrt{3}$ .

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Problem 52

A car with mass $800 \mathrm{~kg}$ traveling at $20 \mathrm{~ms}^{-1}$ sees a dog $50 \mathrm{~m}$ ahead. Can it stop?

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Problem 53

Find the sum of the perimeters of the four triangles formed by the diagonals of square $A B C D$ . Choices: A. $2+2 \sqrt{2}$ B. $8+4 \sqrt{2}$ C. $8+8 \sqrt{2}$ D. 16

See Solution

Problem 54

Find the value of $x$ where the function $f(x)=(x-10)(x+13)$ reaches its minimum. A. -130 B. -13 C. $-\frac{23}{2}$ D. $-\frac{3}{2}$

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Problem 55

Solve the equations: $3x - 9 = 4x + 5$ , $3 - 9 = 4x + 5$ , $3x = 4x + 7 + 3$ .

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Problem 56

Solve the equation: $1 - 2x = 0$ .

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Problem 57

See Solution

Problem 58

Deux amis comparent leurs frais de parking : 2,50€ pour 50 min et 3,50€ pour 1 h 10 min. Le prix est-il proportionnel au temps ?

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Problem 59

Un commerçant applique une réduction de $45\%$ . Quelle formule pour la réduction en B2 et le prix après en B3 ? Prix soldé : $33€$ . Prix initial ?

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Problem 60

Deux amis comparent le coût du parking: 2,50 € pour 50 min et 3,50 € pour 1 h 10 min. Le prix est-il proportionnel au temps?

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Problem 61

Find the derivative of $y$ with respect to $x$ for the expression $x+\ln |x-3|+\frac{2}{x-3}$ .

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Problem 62

Express the polynomial $\frac{5}{2} x^{3}+3 x^{4}+\frac{7}{2} x^{5}+4 x^{6}$ in sigma notation. Which option is correct?

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Problem 63

Which statement is TRUE? A: $\sum_{i=1}^{n} 2 x_{i}=2 \sum_{i=1}^{n} x_{i}$ or B: $\sum_{i=1}^{n}(x_{i})^{2}=(\sum_{i=1}^{n} x_{i})^{2}$ ? Choose: a. A only, b. Neither, c. Both, d. B only.

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Problem 64

Find the formula for the marginal average profit of the profit function $P(x)=100 \ln (2 x+1)-5 x-10$ . Options are provided.

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Problem 65

Find the point elasticity of demand for cellphones at the price $p=4600$ , given the demand function $q=85000-4p$ .

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Problem 66

Anthony turned $90^{\circ}$ right, then $90^{\circ}$ , and $135^{\circ}$ more. Did he complete a circle? How much more to finish?

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Problem 67

Find eigenvalues for the generalized eigenvalue problem involving matrices $K$ , $M$ , and transformations to standard form.

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Problem 68

Find the excess supply of jeans when the price is set at \ $R 650, given demand$ p_{d}=500-2 q_{d} $and supply$ p_{s}=-30+8 q_{s}$.

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Problem 69

Identify which option is not a subset of real numbers: Natural numbers, Whole numbers, Rational numbers, or none of the above.

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Problem 70

Identify the even number from this list: 113-144, $330-366$ , 471-510, $890-899$ .

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Problem 71

Identify the odd number from this list: 782, 984, 102, 633.

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Problem 72

Choose three numbers less than 12.13 from the options: A. 12.146 B. 12.025 C. 12.5 D. 12.103 E. 12.072.

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Problem 73

Given a table of student activities, find the probability a senior is in sports:
$P(\text{sports} \mid \text{senior}) = \frac{P(\text{sports and senior})}{P(\text{senior})} = [?]\%$
Round to the nearest whole percent.

See Solution

Problem 74

Given a class table, find the probability a student is a sophomore if they are female:
$P(\text{sophomore} \mid \text{female}) = \frac{P(\text{sophomore and female})}{P(\text{female})} = [?] \%$
Round to the nearest whole percent.

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Problem 75

Find the probability a sophomore is in drama: $\mathrm{P}(\text{drama} \mid \text{sophomore}) = \frac{\mathrm{P}(\text{drama and sophomore})}{\mathrm{P}(\text{sophomore})} = [?]\%$ . Round to the nearest whole percent.

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Problem 76

A two-way table shows students by gender and class. Find the probability a student is a junior given they are male:
$\mathrm{P}(\text { junior } \mid \text { male })=[?] \%$ Round to the nearest whole percent.

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Problem 77

La distance de freinage $d$ d'un véhicule est-elle proportionnelle à $v$ ou à $v^2$ avec $d(v)=0,005 v^{2}$ ?

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Problem 78

Une piscine de dimensions $30 \mathrm{dm} \times 54 \mathrm{dm}$ doit être recouverte de carreaux carrés.
(a) Décompose $30$ en facteurs premiers. (b) Décompose $54$ en facteurs premiers. (c) Quel est le plus grand diviseur commun de $30$ et $54$ ?
Quelle est la taille maximale des carreaux en dm et combien en faut-il pour couvrir le fond ?

See Solution

Problem 79

Sur une route sèche, la distance de freinage $d(v)=0,005 v^{2}$ . Est-elle proportionnelle à $v$ ou à $v^{2}$ ?

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Problem 80

Find the largest common factor of $3 x^{3} y + 2 x^{2} y^{2}$ . Options: a) $6 x^{3} y^{2}$ , b) $6 x^{5} y^{3}$ , c) $x^{2} y$ , d) $x^{3} y^{2}$ , e) $2 x^{2} y$ .

See Solution

Problem 81

Identify the decreasing exponential function with a $y$ -intercept of 20 from these options: (1) $y=20\left(\frac{4}{3}\right)^{x}$ (2) $y=20\left(\frac{1}{2}\right)^{x}$ (3) $y=-2 x+20$ (4) $y=\left(\frac{1}{3}\right)^{x}+20$

See Solution

Problem 82

If $|x-3|>5$ , which inequalities are true? a) $-2<x<8$ b) $-8<x<2$ c) $x<-8 \cup x>2$ d) $x<-2 \cup x>8$ e) $x<-8 \cup x>-2$

See Solution

Problem 83

Solve $2 x^{2}-8 \leq 0$ and choose the correct interval for $x$ .

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Problem 84

Which function best fits the data: $y=10 x+2$ , $y=8 x+2$ , $y=5(2)^{x}$ , or $y=2(5)^{x}$ ? Data: $(0,2), (1,10), (2,50), (3,250), (4,1250)$ .

See Solution

Problem 85

Factor $16 x^{4}-1$ . Choose the correct option from: a) $(2 x-1)^{2}(2 x+1)^{2}$ , b) $(4 x-1)^{2}(4 x+1)^{2}$ , c) $(2 x-1)(2 x+1)(4 x^{2}+1)$ , d) $(2 x-1)(2 x+1)(2 x^{2}-1)$ , e) $(2 x-1)(2 x+1)(2 x^{2}+1)$ .

See Solution

Problem 86

1. For the function $f(x)=10(2)^{x}$ , find $f(0)$ and its graph point. Is it increasing or decreasing? Compare average rates with $g(x)=10x+7$ . Sketch the graph.

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Problem 87

If $A$ and $B$ are invertible square matrices, find $(A B)^{-1}$ .

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Problem 88

The graph of $y=4-x$ is: a) parabola, b) parabola, c) line (slope -1, intercept 4), d) line (slope 4, intercept -1), e) circle.

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Problem 89

The graph of $y=4-x^{2}$ is: a) down parabola at $(0,4)$ , b) down at $(4,0)$ , c) up at $(0,4)$ , d) up at $(4,0)$ , e) circle radius 2.

See Solution

Problem 90

Circle the highlighted digit and state its value:
4. $2,850,12$ tens
5. $2,905,146$ hundred thousands

See Solution

Problem 91

What is the domain restriction for the equation $y=-a \sqrt{x-d}+c$ ?

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Problem 92

Find the number of intersection points for the system: $y=ax+8$ and $y=-x^{2}$ .

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Problem 93

Find the Discriminant of the equation $y=5 x^{2}-5 x+10$ .

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Problem 94

If $S(t)=250(1.045)^{t}$ , which statement is true about the initial deposit and interest rate?

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Problem 95

If a triangle is scalene, then all side lengths are different. Choose the equivalent statement: A, B, or C.

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Problem 96

If $S(t)=250(1.045)^{t}$ , which statement about the initial deposit and interest rate is true?

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Problem 97

Determine which sets can be side lengths of a triangle: A. $9,5,15$ B. $10,3,7$ C. $8,5,7$

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Problem 98

Find the Discriminant of the quadratic equation $y=3 x^{2}-5 x+2$ .

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Problem 99

Identify the domain restriction for the function $y=-a \sqrt{x-d}+c$ . What is the restriction?

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Problem 100

What is the domain restriction for the function $y=\frac{a}{x-d}+c$ ?

See Solution

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Analyze

Problem 1

Find when balls A and B, rotating at different speeds, meet at the starting point again. A: 2 rotations in 26 min, B: 5 in 35 min.

Problem 2

Problem 3

Find when balls A and B, with rotation times of 26/2 and 35/5 minutes, meet at the starting point again.

Problem 4

In the 2017 Wyoming senate of 30 members, find the inequality for Democrats d d d and Republicans r r r for a bill to pass: A) d+r>15 d+r>15 d+r>15 B) d+r<15 d+r<15 d+r<15 C) d+r≥15 d+r \geq 15 d+r≥15 D) d+r≤15 d+r \leq 15 d+r≤15

Problem 5

In the 2017 Wyoming state senate of 30 members, what inequality shows d+r>15 d + r > 15 d+r>15 for a bill to pass? A) d+r>15 d+r>15 d+r>15 B) d+r<15 d+r<15 d+r<15 C) d+r≥15 d+r \geq 15 d+r≥15 D) d+r≤15 d+r \leq 15 d+r≤15

Problem 6

Find the focus of the parabola x=y2+4y+10 x = y^{2} + 4y + 10 x=y2+4y+10. Choose from: (−6.25,2) (-6.25,2) (−6.25,2), (−2,6.25) (-2,6.25) (−2,6.25), (6.25,−2) (6.25,-2) (6.25,−2), (2,6.25) (2,6.25) (2,6.25).

Problem 7

Find k k k such that x2+k(x+2)+3(x+1)>0 x^{2}+k(x+2)+3(x+1)>0 x2+k(x+2)+3(x+1)>0 for all x x x. What is the range of k k k?

Problem 8

Find the largest prime k k k such that x2+6x+25−2kx>0 x^{2} + 6x + 25 - 2kx > 0 x2+6x+25−2kx>0 for all real x x x.

Problem 9

Find the derivative of x2 x^{2} x2 with respect to x x x.

Problem 10

In triangle DEF D E F DEF, find the longest side given m∠D=59∘,m∠E=76∘,m∠F=45∘ m \angle D=59^{\circ}, m \angle E=76^{\circ}, m \angle F=45^{\circ} m∠D=59∘,m∠E=76∘,m∠F=45∘.

Problem 11

Find the ball's instantaneous velocity at t=10.0 t=10.0 t=10.0 s given x(t)=0.000015t5−0.004t3+0.4t x(t)=0.000015 t^{5}-0.004 t^{3}+0.4 t x(t)=0.000015t5−0.004t3+0.4t.

Problem 12

Determine if the series converges or diverges: ∑n=1∞[(67)n−32n]\sum_{n=1}^{\infty}\left[\left(\frac{6}{7}\right)^{n}-\frac{3}{2^{n}}\right]n=1∑∞​[(76​)n−2n3​]. If it converges, find the sum.

Problem 13

Problem 14

Problem 15

Problem 16

Find the values of k k k such that the curve y=x2−4x+kx+3 y=x^{2}-4x+kx+3 y=x2−4x+kx+3 is above the line y+3x=2 y+3x=2 y+3x=2.

Problem 17

What time is nearest to midnight: A. 11:55 a.m., B. 12:06 a.m., C. 11:50 a.m., D. 12:03 a.m.?

Problem 18

Find the range of values of k k k for which the curve y=x2−4x+kx+3 y=x^{2}-4 x+k x+3 y=x2−4x+kx+3 is above the line y+3x=2 y+3 x=2 y+3x=2.

Problem 19

Find a a a and b b b if the line y=x+h y=x+h y=x+h is tangent to y=k1−x y=\frac{k}{1-x} y=1−xk​ and k=(h+a)2b k=\frac{(h+a)^{2}}{b} k=b(h+a)2​.

Problem 20

Find values of k k k so that 2x2+k2+2−2(k+2)x>0 2 x^{2}+k^{2}+2-2(k+2) x > 0 2x2+k2+2−2(k+2)x>0 for all x x x.

Problem 21

Find the derivative ddx(tan⁡(ln⁡(x))) \frac{d}{d x}(\tan (\ln (x))) dxd​(tan(ln(x))). What is dydx \frac{d y}{d x} dxdy​ for x+y2=xy+2 \sqrt{x}+y^{2}=x y+2 x​+y2=xy+2 at (4,0)?

Problem 22

A particle's velocity is v(t)=et−1−3sin⁡(t−1) v(t)=e^{t-1}-3 \sin (t-1) v(t)=et−1−3sin(t−1). What is its motion at t=1 t=1 t=1? (a) speeding up, (b) slowing down, (c) neither, (d) at rest.

Problem 23

At t=2 t=2 t=2, what does R′(2)=4 R^{\prime}(2)=4 R′(2)=4 mean? (a) Depth is 4 inches. (b) Rate is 4 in/hr. (c) Rate of change is 4 in/hr². (d) Depth increased by 4 inches.

Problem 24

Problem 25

Which type of triangle cannot be both obtuse and one of the following: equilateral, acute, isosceles, or scalene?

Problem 26

Which type of triangle cannot be both scalene and acute, right and acute, equilateral and acute, or isosceles and acute?

Problem 27

已知 z=1−2i z=1-2 i z=1−2i 且 z+a⋅zˉ+b=0 z+a \cdot \bar{z}+b=0 z+a⋅zˉ+b=0，求 a a a 和 b b b 的值。选项为 A. a=1,b=−2 a=1, b=-2 a=1,b=−2 B. a=−1,b=2 a=-1, b=2 a=−1,b=2 C. a=1,b=2 a=1, b=2 a=1,b=2 D. a=−1,b=−2 a=-1, b=-2 a=−1,b=−2。

Problem 28

Identify the point that does not lie on the line formed by 3 of the following points: (−2,−3)(-2,-3)(−2,−3), (3,2)(3,2)(3,2), (−1,0)(-1,0)(−1,0), (−3,−4)(-3,-4)(−3,−4).

Problem 29

已知半径为1的球体，求四棱锥体积最大时的高度选项：A. 13 \frac{1}{3} 31​ B. 12 \frac{1}{2} 21​ C. 33 \frac{\sqrt{3}}{3} 33​​ D. 22 \frac{\sqrt{2}}{2} 22​​

Problem 30

Express tan⁡35∘+tan⁡55∘ \tan 35^{\circ}+\tan 55^{\circ} tan35∘+tan55∘ using k k k if cos⁡35∘=k \cos 35^{\circ}=k cos35∘=k.

Problem 31

Calculate the total fuel cost from the transaction: 35.270 L at \$1.619/L, with HST included of \$6.57. Total: \$57.10.

Problem 32

Identify the property shown: EK+KF=KE+FK E K + K F = K E + F K EK+KF=KE+FK - multiplication, transitive, subtraction, reflexive, or none?

Problem 33

Identify the property shown: BK+KF=KE+FK BK + KF = KE + FK BK+KF=KE+FK (options: multiplication, transitive, subtraction, reflexive, none).

Problem 34

Solve the equation: x2−16x+61=2x−20x^{2}-16 x+61=2 x-20x2−16x+61=2x−20.

Problem 35

In a survey of 400 Grade 7 students, find how many play both ML \mathrm{ML} ML and COD \mathrm{COD} COD using a Venn diagram.

Problem 36

Problem 37

Identify the function: y=−16xy=-16xy=−16x. Is it a step, constant, absolute value, or direct variation function?

Problem 38

Identify the property shown in 3x(y+2)=(y+2)3x3 x(y+2)=(y+2) 3 x3x(y+2)=(y+2)3x: distributive, identity, commutative, or associative?

Problem 39

Medina dan Adi bermain catur. Medina menang 3 kali dan draw 2 kali. Apakah pernyataan berikut benar atau salah? 1. Skor Adi = 212. Skor Medina = 443. Total skor = 52

Problem 40

Medina menang 3 kali dan draw 2 kali. Cek kebenaran pernyataan: Skor Adi 21, Skor Medina 44, Total skor 52.

Problem 41

Find series turns per pole for a compound generator to keep V=618 VV = 618 \mathrm{~V}V=618 V with loads of 4 A4 \mathrm{~A}4 A and 5.5 A5.5 \mathrm{~A}5.5 A. Shunt turns: 2700.

Problem 42

Problem 43

Which expression for yyy comes from the system: 5x−8y=175x - 8y = 175x−8y=17 and −8x−3y=−43-8x - 3y = -43−8x−3y=−43?

In the 2017 Wyoming senate of 30 members, find the inequality for Democrats $d$ and Republicans $r$ for a bill to pass:
A) $d+r>15$
B) $d+r<15$
C) $d+r \geq 15$
D) $d+r \leq 15$

In the 2017 Wyoming state senate of 30 members, what inequality shows $d + r > 15$ for a bill to pass? A) $d+r>15$ B) $d+r<15$ C) $d+r \geq 15$ D) $d+r \leq 15$

Find the focus of the parabola $x = y^{2} + 4y + 10$ . Choose from: $(-6.25,2)$ , $(-2,6.25)$ , $(6.25,-2)$ , $(2,6.25)$ .

Find $k$ such that $x^{2}+k(x+2)+3(x+1)>0$ for all $x$ . What is the range of $k$ ?

Find the largest prime $k$ such that $x^{2} + 6x + 25 - 2kx > 0$ for all real $x$ .

Find the derivative of $x^{2}$ with respect to $x$ .

In triangle $D E F$ , find the longest side given $m \angle D=59^{\circ}, m \angle E=76^{\circ}, m \angle F=45^{\circ}$ .

Find the ball's instantaneous velocity at $t=10.0$ s given $x(t)=0.000015 t^{5}-0.004 t^{3}+0.4 t$ .

Determine if the series converges or diverges: $\sum_{n=1}^{\infty}\left[\left(\frac{6}{7}\right)^{n}-\frac{3}{2^{n}}\right]$ . If it converges, find the sum.

Find the values of $k$ such that the curve $y=x^{2}-4x+kx+3$ is above the line $y+3x=2$ .

Find the range of values of $k$ for which the curve $y=x^{2}-4 x+k x+3$ is above the line $y+3 x=2$ .

Find $a$ and $b$ if the line $y=x+h$ is tangent to $y=\frac{k}{1-x}$ and $k=\frac{(h+a)^{2}}{b}$ .

Find values of $k$ so that $2 x^{2}+k^{2}+2-2(k+2) x > 0$ for all $x$ .

Find the derivative $\frac{d}{d x}(\tan (\ln (x)))$ . What is $\frac{d y}{d x}$ for $\sqrt{x}+y^{2}=x y+2$ at (4,0)?

A particle's velocity is $v(t)=e^{t-1}-3 \sin (t-1)$ . What is its motion at $t=1$ ? (a) speeding up, (b) slowing down, (c) neither, (d) at rest.

At $t=2$ , what does $R^{\prime}(2)=4$ mean? (a) Depth is 4 inches. (b) Rate is 4 in/hr. (c) Rate of change is 4 in/hr². (d) Depth increased by 4 inches.

已知 $z=1-2 i$ 且 $z+a \cdot \bar{z}+b=0$ ，求 $a$ 和 $b$ 的值。选项为 A. $a=1, b=-2$ B. $a=-1, b=2$ C. $a=1, b=2$ D. $a=-1, b=-2$ 。

Identify the point that does not lie on the line formed by 3 of the following points: $(-2,-3)$ , $(3,2)$ , $(-1,0)$ , $(-3,-4)$ .

已知半径为1的球体，求四棱锥体积最大时的高度选项：A. $\frac{1}{3}$ B. $\frac{1}{2}$ C. $\frac{\sqrt{3}}{3}$ D. $\frac{\sqrt{2}}{2}$

Express $\tan 35^{\circ}+\tan 55^{\circ}$ using $k$ if $\cos 35^{\circ}=k$ .

Identify the property shown: $E K + K F = K E + F K$ - multiplication, transitive, subtraction, reflexive, or none?

Identify the property shown: $BK + KF = KE + FK$ (options: multiplication, transitive, subtraction, reflexive, none).

Solve the equation: $x^{2}-16 x+61=2 x-20$ .

In a survey of 400 Grade 7 students, find how many play both $\mathrm{ML}$ and $\mathrm{COD}$ using a Venn diagram.

Identify the function: $y=-16x$ . Is it a step, constant, absolute value, or direct variation function?

Identify the property shown in $3 x(y+2)=(y+2) 3 x$ : distributive, identity, commutative, or associative?

Medina dan Adi bermain catur. Medina menang 3 kali dan draw 2 kali. Apakah pernyataan berikut benar atau salah?
1. Skor Adi = 21
2. Skor Medina = 44
3. Total skor = 52

Find series turns per pole for a compound generator to keep $V = 618 \mathrm{~V}$ with loads of $4 \mathrm{~A}$ and $5.5 \mathrm{~A}$ . Shunt turns: 2700.

Which expression for $y$ comes from the system: $5x - 8y = 17$ and $-8x - 3y = -43$ ?

Ibrahim dan Zahra datang bersama pada 2 Juli 2022. Kapan mereka akan bersama lagi? Tandai dengan $\sqrt{ }$ pilihanmu!
1. 12 Juli 2022
2. 14 Juli 2022
3. 26 Juli 2022
4. 7 Agustus 2022

Analyze a lever with a pivot force of 30N. Left: 4N at 1m, 7N at 4m. Right: 7N at 3m. Determine:
a) Are moments in equilibrium? b) Are forces in equilibrium? c) Is the lever in equilibrium?

Digite o número que falta na sequência: $1, 2, \square, 8, 16, 32$ .

Analyze how a student could mistakenly choose each incorrect answer for the system of equations: $x - 2y = 2$ and $2x + y = 9$ .

Solve the differential equation: $x y \, dx - (x+2) \, dy = 0$ .

Find the equivalent expression for $9^{\frac{3}{4}}$ from the options: A) $\sqrt[3]{9}$ B) $\sqrt[4]{9}$ C) $\sqrt{3}$ D) $3 \sqrt{3}$ .

A car with mass $800 \mathrm{~kg}$ traveling at $20 \mathrm{~ms}^{-1}$ sees a dog $50 \mathrm{~m}$ ahead. Can it stop?

Find the sum of the perimeters of the four triangles formed by the diagonals of square $A B C D$ . Choices: A. $2+2 \sqrt{2}$ B. $8+4 \sqrt{2}$ C. $8+8 \sqrt{2}$ D. 16

Find the value of $x$ where the function $f(x)=(x-10)(x+13)$ reaches its minimum. A. -130 B. -13 C. $-\frac{23}{2}$ D. $-\frac{3}{2}$

Solve the equations: $3x - 9 = 4x + 5$ , $3 - 9 = 4x + 5$ , $3x = 4x + 7 + 3$ .

Solve the equation: $1 - 2x = 0$ .

Un commerçant applique une réduction de $45\%$ . Quelle formule pour la réduction en B2 et le prix après en B3 ? Prix soldé : $33€$ . Prix initial ?

Find the derivative of $y$ with respect to $x$ for the expression $x+\ln |x-3|+\frac{2}{x-3}$ .

Express the polynomial $\frac{5}{2} x^{3}+3 x^{4}+\frac{7}{2} x^{5}+4 x^{6}$ in sigma notation. Which option is correct?

Find the formula for the marginal average profit of the profit function $P(x)=100 \ln (2 x+1)-5 x-10$ . Options are provided.

Find the point elasticity of demand for cellphones at the price $p=4600$ , given the demand function $q=85000-4p$ .

Anthony turned $90^{\circ}$ right, then $90^{\circ}$ , and $135^{\circ}$ more. Did he complete a circle? How much more to finish?

Find eigenvalues for the generalized eigenvalue problem involving matrices $K$ , $M$ , and transformations to standard form.

Find the excess supply of jeans when the price is set at \ $R 650, given demand$ p_{d}=500-2 q_{d} $and supply$ p_{s}=-30+8 q_{s}$.

Identify the even number from this list: 113-144, $330-366$ , 471-510, $890-899$ .