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2 years ago

Q # 17 please solve the figures

Mathematics

1 answer:

Juliette [100K]2 years ago

6 0

Answer: First option:
Angle C is congruent with angle X, angle D is congruent with angle Y, angle A is congruent with angle Z

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This year’s school population in Waterloo is 135 percent of last year’s school population. This year’s student population is 756

sp2606 [1]

Answer:560

Step-by-step explanation:

Let a be the number of students the school have last year

135% of a=756

135/100 x a=756

135a/100=756

Cross multiplying we get

135a=756 x100

135a=75600

Divide both sides by 135

135a/135=75600/135

a=560

6 0

2 years ago

Solve the following differential equation: y" + y' = 8x^2

PtichkaEL [24]

Answer:

$y=y_p+y_h = \frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$

Step-by-step explanation:

Let's find a particular solution. We need a function of the form $y= ax^3+bx^2+cx+d$ such that

$y'= 3ax^2+2bx+c$ and

$y''= 6ax+2b$

$y'+y''= 3ax^2+2bx+c+6ax+2b = 3ax^2+x(2b+6a)+(c+2b) = 8x^2$

then, 3a= 8, 2b+6a =0 and c+2b = 0. With the first equation we obtain

a = 8/3 and replacing in the second equation 2b+6(8/3) = 2b + 16 = 0. Then, b = -8. Finally, c = -2(-8) = 16.

So, our particular solution is $y_p= \frac{8}{3}x^3-8x^2+16x$ .

Now, let's find the solution $y_p$ of the homogeneus equation $y''+y'=0$ with the method of constants coefficients. Let $y=e^{\lambda x}$

$y'=\lambda e^{\lambda x}$

$y''=\lambda^2e^{\lambda x}$

then $\lambda e^{\lambda x}+\lambda^2 e^{\lambda x} = 0$

$e^{\lambda x}(\lambda +\lambda^2)= 0$

$(\lambda +\lambda^2)= 0$

$\lambda (1+\lambda)= 0$

$\lambda =0$ and $\lambda)= -1$ .

So, $y_h = C_1 + C_2e^{-x}$ and the solution is

$y=y_p+y_h =\frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$ .

5 0

2 years ago

Simply 2 1/2 divided by 1 1/3

alexgriva [62]

Answer:

15.8 (15/8)

Step-by-step explanation:

First, we turn the mixed numbers into fractions by multiplying the whole number by the denominator and this answer into the numerator:

2 1/2=5/2

1 1/3=4/3

now to divide, we keep the first fraction, change the divide to a multiply, and then flip the second fraction:

5/2·3/4

Now, simply multiply:

5/2·3/4=15/8 (15.8 if you need a decimal)

And you have your answer! hope this helped!

5 0

2 years ago

3. QR find the arc length 02.83 021.99 O 12.57 0 34.56

jeka94

Your answer should be 12.57

8 0

2 years ago

Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypot

Nina [5.8K]

Answer: a. 0.1031; fail to reject the null hypothesis

Step-by-step explanation:

Given: Significance level : $\alpha=0.05$

The test statistic in a two-tailed test is z = -1.63.

The P-value for two-tailed test : $2P(Z>|z|)=2P(Z>|-1.63|)=0.1031$ [By p-value table]

Since, 0.1031 > 0.05

i.e. p-value > $\alpha$

So, we fail to reject the null hypothesis. [When p< $\alpha$ then we reject null hypothesis ]

So, the correct option is a. 0.1031; fail to reject the null hypothesis.

8 0

2 years ago